It is known to use so-called pivotal attachments of this kind for the purpose of attaching an object to a supporting surface while enabling the object to be moved to different positional settings and angular positions in relation to the supporting surface. The known attachments, however, are encumbered with certain drawbacks. For instance, it is necessary with these attachments to screw down the nut very tightly in order to achieve a stable attachment, i.e. in order to ensure that the object will not move out of its set position. Another drawback is the risk that these known attachments will fasten in one set position from which the attachment cannot be moved, due to the fact that the spherical body has become clamped or pinched in the lower part of the attachment assembly, partly as a result of the large tightening force applied to the nut and partly because of the unsuitable configuration of the dished recess.